How do you simplify #(21-3x)/( 9x- 64x^3)#?

1 Answer
Oct 24, 2017

Answer:

#(3(7-x))/(x(3-8x)(3+8x))#

Explanation:

#"factorise the numerator/denominator and cancel any"#
#color(blue)"common factors"#

#•color(white)(x)21-3x=3(7-x)larrcolor(blue)"common factor of 3"#

#•color(white)(x)9x-64x^3=x(9-64x^2)larrcolor(blue)"common factor of x"#

#"note that "9-64x^2color(blue)" is a difference of squares"#

#•color(white)(x)a^2-b^2=(a-b)(a+b)#

#"here "a=3" and "b=8x#

#rArr9-64x^2=(3-8x)(3+8x)#

#rArr(21-3x)/(9x-64x^3)#

#=(3(7-x))/(x(3-8x)(3+8x))to(x!=0,x!=+-3/8)#